Abstract
In this paper we study rings of differential operators for modules of covariants for one-dimensional tori. In particular we analyze when they are Morita equivalent, when they are simple, and when they have finite global dimension. As a side result we obtain an extension of the Bernstein-Beilinson equivalence to weighted projective spaces.
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References
I.N. Bernstein, I.M. Gelfand and S.I. Gelfand, Differential operators on the cubic cone, Russian Math. Surveys 27 (1972), 169–174.
M. Chamarie, Sur les ordres maximaux au sens d'Asano, Vorlesungen aus den Fachbereich Mathematik, Universität Essen, Heft 3 (1979).
S.C. Coutinho, M.P. Holland, Differential operators on smooth varieties, to appear.
A. Grothendieck, Cohomologie locale de faisceaux cohérent et théorèmes de Lefschetz locaux et globaux, North Holland (1968).
T. Hodges, P. Smith, Differential operators on projective space, Univ, of Cincinnati preprint.
T. Hodges, P. Smith, Rings of differential operators and the Beilinson-Bernstein equivalence of categories, Proc. Amer. Math. Soc. 93, 379–386.
J.M. Kantor, Formes et opérateurs différentiels sur les espaces analytiques complexes, Bull. Soc. Math. France, Mémoire 53 (1977), 5–80.
T. Levasseur, Relèvements d'opérateurs différentiels sur les anneaux d'invariants, Progress in Mathematics, Vol. 92, 449–470 (1990).
T. Levasseur and J.T. Stafford, Rings of differential operators on classical rings of invariants, Memoirs of the AMS 412 (1989).
J.C. McConnel, J.C. Robson, Noncommutative Noetherian rings, John Wiley & Sons, New-York (1987).
I. Musson, Rings of differential operators on invariant rings of tori, Trans. Amer. Math. Soc. 303 (1987), 805–827.
G. Schwartz, Lifting differential operators from orbit spaces, to appear.
R.P. Stanley, Linear diophantine equations and local cohomology, Invent. Math. 68, 175–193, (1982).
R.P. Stanley, Combinatorics and invariant theory, Proc. Symp. Pure Math., Vol. 34, (1979).
M. Van den Bergh, Cohen-Macaulayness of semi-invariants for tori, to appear in Trans. Amer. Math. Soc.
M. Van den Bergh, Cohen-Macaulayness of modules of covariants, to appear in Invent. Math.
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© 1991 Springer-Verlag
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Van den Bergh, M. (1991). Differential operators on semi-invariants for tori and weighted projective spaces. In: Topics in Invariant Theory. Lecture Notes in Mathematics, vol 1478. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083507
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DOI: https://doi.org/10.1007/BFb0083507
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